Connect vertex after bevel
Use the Knife tool (K) instead to cut more edges. I'm new to Blender too, but it seems that F (make edge/face) is for building up new mesh in space, not for cutting new edges in existing geometry. When you choose two vertices and make an edge between them with F, it doesn't seem as if the new edge is connected to the face it crosses.  Correct me if I'm wrong someone.